<html><head><title>The GAP 4 Reference Manual - References</title></head> <body text="#000000" bgcolor="#ffffff"> <h1>The <font face="Gill Sans,Helvetica,Arial">GAP</font> 4 Reference Manual - References</h1><dl> <dt><a name="AMW82"><b>[AMW82]</b></a><dd> D[avid] G. Arrell, S[anjiv] Manrai, and M[ichael] F. Worboys. <br> A procedure for obtaining simplified defining relations for a subgroup. <br> In Campbell and Robertson <a href="#GrpsStAndrews81"><cite>GrpsStAndrews81</cite></a>, pages 155--159. <dt><a name="AR84"><b>[AR84]</b></a><dd> D[avid] G. Arrell and E[dmund] F. Robertson. <br> A modified Todd-Coxeter algorithm. <br> In Atkinson <a href="#Durham1982"><cite>Durham1982</cite></a>, pages 27--32. <dt><a name="Art68"><b>[Art68]</b></a><dd> E[mil] Artin. <br> <em>Galoissche Theorie</em>. <br> Verlag Harri Deutsch, Frankfurt/Main, 1968. <dt><a name="Durham1982"><b>[Durham1982]</b></a><dd> Michael D. Atkinson, editor. <br> <em>Computational Group Theory, Proceedings LMS Symposium on Computational Group Theory, Durham 1982</em>. Academic Press, 1984. <dt><a name="Baker84"><b>[Baker84]</b></a><dd> Alan Baker. <br> <em>A concise introduction to the theory of numbers</em>. <br> Cambridge University Press, 1984. <dt><a name="BC76"><b>[BC76]</b></a><dd> M[ichael] J. Beetham and C[olin] M. Campbell. <br> A note on the Todd-Coxeter coset enumeration algorithm. <br> <em>Proc. Edinburgh Math. Soc. Edinburgh Math. Notes</em>, 20:73--79, 1976. <dt><a name="BC89"><b>[BC89]</b></a><dd> Richard P. Brent and Graeme L. Cohen. <br> A new lower bound for odd perfect numbers. <br> <em>Math. Comp.</em>, 53:431--437, 1989. <dt><a name="BC94"><b>[BC94]</b></a><dd> Ulrich Baum and Michael Clausen. <br> Computing irreducible representations of supersolvable groups. <br> <em>Math. Comput.</em>, 207:351--359, 1994. <dt><a name="BCFS91"><b>[BCFS91]</b></a><dd> L[ászló] Babai, G[ene] Cooperman, L[arry] Finkelstein, and Á[kos] Seress. <br> Nearly linear time algorithms for permutation groups with a small base. <br> In <em>Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC'91), Bonn 1991</em>, pages 200--209. ACM Press, 1991. <dt><a name="BescheEick98"><b>[BescheEick98]</b></a><dd> Hans Ulrich Besche and Bettina Eick. <br> Construction of finite groups. <br> <em>J. Symbolic Comput.</em>, 27(4):387--404, 1999. <dt><a name="BescheEick1000"><b>[BescheEick1000]</b></a><dd> Hans Ulrich Besche and Bettina Eick. <br> The groups of order at most 1000 except 512 and 768. <br> <em>J. Symbolic Comput.</em>, 27(4):405--413, 1999. <dt><a name="BescheEick768"><b>[BescheEick768]</b></a><dd> Hans Ulrich Besche and Bettina Eick. <br> The groups of order <i>q</i><sup><i>n</i></sup> ·<i>p</i>. <br> <em>Comm. Alg.</em>, 29(4):1759--1772, 2001. <dt><a name="BEO00"><b>[BEO00]</b></a><dd> Hans Ulrich Besche, Bettina Eick, and E. A. O'Brien. <br> The groups of order at most 2000. <br> <em>Electronic Research Announcements of the AMS</em>, 7:1 -- 4, 2001. <dt><a name="BEO01"><b>[BEO01]</b></a><dd> Hans Ulrich Besche, Bettina Eick, and E. A. O'Brien. <br> A millenium project: constructing small groups. <br> <em>IJAC</em>, 12:623 -- 644, 2002. <dt><a name="Ber76"><b>[Ber76]</b></a><dd> T. R. Berger. <br> Characters and derived length in groups of odd order. <br> <em>J. Algebra</em>, 39:199--207, 1976. <dt><a name="Besche92"><b>[Besche92]</b></a><dd> Hans Ulrich Besche. <br> Die Berechnung von Charaktergraden und Charakteren endlicher auflösbarer Gruppen im Computeralgebrasystem GAP. <br> Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1992. <dt><a name="BFS79"><b>[BFS79]</b></a><dd> F. Rudolf Beyl, Ulrich Felgner, and Peter Schmid. <br> On groups occurring as center factor groups. <br> <em>J. Algebra</em>, 61(1):161--177, 1979. <dt><a name="BJR87"><b>[BJR87]</b></a><dd> R. Brown, D. L. Johnson, and E. F. Robertson. <br> Some computations of nonabelian tensor products of groups. <br> <em>J. Algebra</em>, 111(1):177--202, 1987. <dt><a name="BreuerLinton98"><b>[BreuerLinton98]</b></a><dd> Thomas Breuer and Steve Linton. <br> The GAP 4 type system. organizing algebraic algorithms. <br> In Gloor <a href="#ISSAC98"><cite>ISSAC98</cite></a>, pages 38--45. <dt><a name="BM83"><b>[BM83]</b></a><dd> Gregory Butler and John McKay. <br> The transitive groups of degree up to 11. <br> <em>Comm. Algebra</em>, 11:863--911, 1983. <dt><a name="Bourbaki70"><b>[Bourbaki70]</b></a><dd> N. Bourbaki. <br> <em>Éléments de Mathématique, Algèbre I</em>, volume 1. <br> Hermann, Paris, 1970. <dt><a name="BP98"><b>[BP98]</b></a><dd> Thomas Breuer and Götz Pfeiffer. <br> Finding Possible Permutation Characters. <br> <em>J. Symbolic Comput.</em>, 26:343--354, 1998. <dt><a name="Bre91"><b>[Bre91]</b></a><dd> Thomas Breuer. <br> Potenzabbildungen, Untergruppenfusionen, Tafel-Automorphismen. <br> Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1991. <dt><a name="Bre97"><b>[Bre97]</b></a><dd> Thomas Breuer. <br> Integral bases for subfields of cyclotomic fields. <br> <em>AAECC</em>, 8:279--289, 1997. <dt><a name="Bre99"><b>[Bre99]</b></a><dd> Thomas Breuer. <br> Computing Possible Class Fusions from Character Tables. <br> <em>Comm. Algebra</em>, 27(6):2733--2748, 1999. <dt><a name="BTW93"><b>[BTW93]</b></a><dd> Bernhard Beauzamy, Vilmar Trevisan, and Paul S. Wang. <br> Polynomial factorization: Sharp bounds, Efficient algorithms. <br> <em>J. Symbolic Comput.</em>, 15:393--413, 1993. <dt><a name="Bur55"><b>[Bur55]</b></a><dd> W[illiam S.] Burnside. <br> <em>Theory of Groups of Finite Order</em>. <br> Dover Publications, New York, 1955. <br> Unabridged republication of the second edition, published in 1911. <dt><a name="Butler93"><b>[Butler93]</b></a><dd> Gregory Butler. <br> The transitive groups of degree fourteen and fifteen. <br> <em>J. Symbolic Comput.</em>, pages 413--422, 1993. <dt><a name="Can73"><b>[Can73]</b></a><dd> John J. Cannon. <br> Construction of defining relators for finite groups. <br> <em>Discrete Math.</em>, pages 105--129, 1973. <dt><a name="Car72a"><b>[Car72a]</b></a><dd> R. W. Carter. <br> <em>Simple groups of Lie type</em>, volume 28 of <em>Pure and Applied Mathematics</em>. <br> John Wiley and Sons, 1972. <dt><a name="CCN85"><b>[CCN85]</b></a><dd> J[ohn] H. Conway, R[obert] T. Curtis, S[imon] P. Norton, R[ichard] A. Parker, and R[obert] A. Wilson. <br> <em>Atlas of finite groups</em>. <br> Oxford University Press, 1985. <dt><a name="ConwayHulpkeMcKay98"><b>[ConwayHulpkeMcKay98]</b></a><dd> John H. Conway, Alexander Hulpke, and John McKay. <br> On transitive permutation groups. <br> <em>LMS J. Comput. Math.</em>, 1:1--8, 1998. <dt><a name="coxlittleoshea"><b>[coxlittleoshea]</b></a><dd> David Cox, John Little, and Donal O'Shea. <br> <em>Ideals, varieties, and algorithms</em>. <br> Undergraduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1997. <br> An introduction to computational algebraic geometry and commutative algebra. <dt><a name="Coh93"><b>[Coh93]</b></a><dd> Henri Cohen. <br> <em>A Course in Computational Algebraic Number Theory</em>, volume 138 of <em>Graduate Texts in Mathematics</em>. <br> Springer, Berlin, Heidelberg and New York, 1993. <dt><a name="Con90a"><b>[Con90a]</b></a><dd> S[am] B. Conlon. <br> Calculating characters of <i>p</i>-groups. <br> <em>J. Symbolic Comput.</em>, 9(5 & 6):535--550, 1990. <dt><a name="Con90b"><b>[Con90b]</b></a><dd> S[am] B. Conlon. <br> Computing modular and projective character degrees of soluble groups. <br> <em>J. Symbolic Comput.</em>, 9(5 & 6):551--570, 1990. <dt><a name="GrpsStAndrews81"><b>[GrpsStAndrews81]</b></a><dd> Colin M. Campbell and Edmund F. Robertson, editors. <br> <em>Groups-St.Andrews 1981, Proceedings of a conference, St.Andrews 1981</em>, volume 71 of <em>London Math. Soc. Lecture Note Series</em>. Cambridge University Press, 1982. <dt><a name="DEi05"><b>[DEi05]</b></a><dd> Heiko Dietrich and Bettina Eick. <br> Groups of cube-free order. <br> <em>Accepted by J. Alg.</em>, 2005. <dt><a name="Dix67"><b>[Dix67]</b></a><dd> J[ohn] D. Dixon. <br> High speed computations of group characters. <br> <em>Numer. Math.</em>, 10:446--450, 1967. <dt><a name="Dix93"><b>[Dix93]</b></a><dd> John D. Dixon. <br> Constructing representations of finite groups. <br> In Larry Finkelstein and William M. Kantor, editors, <em>Proceedings of the 1991 DIMACS Workshop on Groups and Computation</em>, volume 11 of <em> DIMACS Series in Discrete Mathematics and Theoretical Computer Science</em>, pages 105--112. American Mathematical Society, 1993. <dt><a name="DixonMortimer88"><b>[DixonMortimer88]</b></a><dd> John D. Dixon and Brian Mortimer. <br> The primitive permutation groups of degree less than 1000. <br> <em>Math. Proc. Cambridge Philos. Soc.</em>, 103:213--238, 1988. <dt><a name="Dre69"><b>[Dre69]</b></a><dd> Andreas [W. M.] Dress. <br> A characterization of solvable groups. <br> <em>Math. Z.</em>, 110:213--217, 1969. <dt><a name="EickHoefling02"><b>[EickHoefling02]</b></a><dd> Bettina Eich and Burkhard H"ofling. <br> The solvable primitive permutation groups of degree at most 6560. <br> submitted, 2002. <dt><a name="Eick97"><b>[Eick97]</b></a><dd> Bettina Eick. <br> Special presentations for finite soluble groups and computing (pre-)Frattini subgroups. <br> In Larry Finkelstein and William M. Kantor, editors, <em>Proceedings of the 2nd DIMACS Workshop held at Rutgers University, New Brunswick, NJ, June 7--10, 1995</em>, volume 28 of <em>DIMACS Series in Discrete Mathematics and Theoretical Computer Science</em>, pages 101--112. American Mathematical Society, 1997. <dt><a name="Ellis98"><b>[Ellis98]</b></a><dd> Graham Ellis. <br> On the capability of groups. <br> <em>Proc. Edinburgh Math. Soc. (2)</em>, 41(3):487--495, 1998. <dt><a name="EOB98"><b>[EOB98]</b></a><dd> Bettina Eick and E. A. O'Brien. <br> The groups of order 512. <br> In Matzat Greuel, Hiss, editor, <em>Proceedings of `Abschlusstagung des DFG Schwerpunktes Algorithmische Algebra und Zahlentheorie in Heidelberg</em>. Springer, 1998. <dt><a name="EOB99"><b>[EOB99]</b></a><dd> Bettina Eick and E. A. O'Brien. <br> Enumerating <i>p</i>-groups. <br> <em>J. Austral. Math. Soc.</em>, 67:191 -- 205, 1999. <dt><a name="FJNT95"><b>[FJNT95]</b></a><dd> V[olkmar] Felsch, D[avid] L. Johnson, J[oachim] Neubüser, and S[ergey] V. Tsaranov. <br> The structure of certain Coxeter groups. <br> In C[olin] M. Campbell, T[haddeus] C. Hurley, E[dmund] F. Robertson, S[ean] J. Tobin, and J[ames] J. Ward, editors, <em>Groups '93 Galway / St.Andrews, Galway 1993, Volume 1</em>, volume 211 of <em>London Math. Soc. Lecture Note Series</em>, pages 177--190. Cambridge University Press, 1995. <dt><a name="FelschNeubueser79"><b>[FelschNeubueser79]</b></a><dd> Volkmar Felsch and Joachim Neubüser. <br> An algorithm for the computation of conjugacy classes and centralizers in <i>p</i>-groups. <br> In Edward W. Ng, editor, <em>Symbolic and Algebraic Computation (Proceedings of EUROSAM 79, An International Symposium on Symbolic and Algebraic Manipulation, Marseille, 1979)</em>, Lecture Notes in Computer Science, 72, pages 452--465. Springer, Berlin, Heidelberg and New York, 1979. <dt><a name="Fra82"><b>[Fra82]</b></a><dd> J[ames] S. Frame. <br> Recursive computation of tensor power components. <br> <em>Bayreuther Math. Schr.</em>, 10:153--159, 1982. <dt><a name="Gir03"><b>[Gir03]</b></a><dd> Boris Girnat. <br> Klassifikation der Gruppen bis zur Ordnung <i>p</i><sup>5</sup>. <br> Staatsexamensarbeit, TU Braunschweig, 2003. <dt><a name="ISSAC98"><b>[ISSAC98]</b></a><dd> Oliver Gloor, editor. <br> <em>Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation</em>. The Association for Computing Machinery, ACM Press, 1998. <dt><a name="Hall"><b>[Hall]</b></a><dd> Marshall Hall, Jr. <br> <em>The theory of Groups</em>. <br> Macmillan, 1959. <dt><a name="Hav69"><b>[Hav69]</b></a><dd> George Havas. <br> Symbolic and algebraic calculation. <br> Basser Computing Dept., Technical Report 89, Basser Department of Computer Science, University of Sydney, Sydney, Australia, 1969. <dt><a name="Hav74b"><b>[Hav74b]</b></a><dd> George Havas. <br> A Reidemeister-Schreier program. <br> In M[ichael] F. Newman, editor, <em>Proceedings of the Second International Conference on the Theory of Groups, Canberra, 1973</em>, volume 372 of <em>Lecture Notes in Math.</em>, pages 347--356. Springer, Berlin, Heidelberg and New York, 1974. <dt><a name="Hup82"><b>[Hup82]</b></a><dd> B[ertram] Huppert and N[orman] Blackburn. <br> <em>Endliche Gruppen II</em>, volume 1242 of <em>Grundlehren Math. Wiss.</em> <br> Springer, Berlin, Heidelberg and New York, 1982. <dt><a name="HIO89"><b>[HIO89]</b></a><dd> Trevor [O.] Hawkes, I. M[artin] Isaacs, and M. Özaydin. <br> On the Möbius function of a finite group. <br> <em>Rocky Mountain J. Math.</em>, 19:1003--1034, 1989. <dt><a name="HJLP92"><b>[HJLP92]</b></a><dd> Gerhard Hiss, Christoph Jansen, Klaus Lux, and Richard [A.] Parker. <br> Computational modular character theory. <br> <a href="http://www.math.rwth-aachen.de/LDFM/homes/MOC/CoMoChaT/">http://www.math.rwth-aachen.de/LDFM/homes/MOC/CoMoChaT/</a>. <dt><a name="HKRR84"><b>[HKRR84]</b></a><dd> George Havas, P[eter] E. Kenne, J[ames] S. Richardson, and E[dmund] F. Robertson. <br> A Tietze transformation program. <br> In Atkinson <a href="#Durham1982"><cite>Durham1982</cite></a>, pages 67--71. <dt><a name="Howie76"><b>[Howie76]</b></a><dd> J. M. Howie. <br> <em>An introduction to semigroup theory</em>. <br> Academic Press [Harcourt Brace Jovanovich Publishers], London, 1976. <br> L.M.S. Monographs, No. 7. <dt><a name="HP89"><b>[HP89]</b></a><dd> Derek F. Holt and W[ilhelm] Plesken. <br> <em>Perfect Groups</em>. <br> Oxford Math. Monographs. Oxford University Press, 1989. <dt><a name="HR94"><b>[HR94]</b></a><dd> Derek [F.] Holt and Sarah Rees. <br> Testing modules for irreducibility. <br> <em>J. Austral. Math. Soc. Ser. A</em>, 57:1--16, 1994. <dt><a name="Hulpke93"><b>[Hulpke93]</b></a><dd> Alexander Hulpke. <br> Zur Berechnung von Charaktertafeln. <br> Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, 1993. <dt><a name="Hulpke96"><b>[Hulpke96]</b></a><dd> Alexander Hulpke. <br> <em>Konstruktion transitiver Permutationsgruppen</em>. <br> Dissertation, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1996. <dt><a name="Hulpke98"><b>[Hulpke98]</b></a><dd> Alexander Hulpke. <br> Computing normal subgroups. <br> In Gloor <a href="#ISSAC98"><cite>ISSAC98</cite></a>, pages 194--198. <dt><a name="Hulpke99"><b>[Hulpke99]</b></a><dd> Alexander Hulpke. <br> Computing subgroups invariant under a set of automorphisms. <br> <em>J. Symbolic Comput.</em>, 27(4):415--427, 1999. <dt><a name="HulpkeClasses"><b>[HulpkeClasses]</b></a><dd> Alexander Hulpke. <br> Conjugacy classes in finite permutation groups via homomorphic images. <br> <em>Math. Comp.</em>, 69(232):1633--1651, 2000. <dt><a name="HulpkeQuot"><b>[HulpkeQuot]</b></a><dd> Alexander Hulpke. <br> Representing subgroups of finitely presented groups by quotient subgroups. <br> <em>Experimental Mathematics</em>, 10(3):369--381, 2001. <dt><a name="HulpkeTG"><b>[HulpkeTG]</b></a><dd> Alexander Hulpke. <br> Constructing transitive permutation groups. <br> <em>J. Symbolic Comput.</em>, 39:1--30, 2005. <dt><a name="Hum72"><b>[Hum72]</b></a><dd> James E. Humphreys. <br> <em>Introduction to Lie algebras and representation theory</em>. <br> Springer-Verlag, New York, 1972. <br> Graduate Texts in Mathematics, Vol. 9. <dt><a name="Hum78"><b>[Hum78]</b></a><dd> James E. Humphreys. <br> <em>Introduction to Lie algebras and representation theory</em>. <br> Springer-Verlag, New York, 1978. <br> Second printing, revised. <dt><a name="Hup67"><b>[Hup67]</b></a><dd> B[ertram] Huppert. <br> <em>Endliche Gruppen I</em>, volume 134 of <em>Grundlehren Math. Wiss.</em> <br> Springer, Berlin, Heidelberg and New York, 1967. <dt><a name="IshibashiEarnest94"><b>[IshibashiEarnest94]</b></a><dd> Hiroyuki Ishibashi and A. G. Earnest. <br> Two-element generation of orthogonal groups over finite fields. <br> <em>J. Algebra</em>, 165(1):164--171, 1994. <dt><a name="Isa76"><b>[Isa76]</b></a><dd> I. M. Isaacs. <br> <em>Character theory of finite groups</em>, volume 69 of <em>Pure and applied mathematics</em>. <br> Academic Press, New York, 1976. <br> xii+303 pp., ISBN 0-12-374550-0. <dt><a name="JLPW95"><b>[JLPW95]</b></a><dd> Christoph Jansen, Klaus Lux, Richard [A.] Parker, and Robert [A.] Wilson. <br> <em>An Atlas of Brauer Characters</em>, volume 11 of <em>London Math. Soc. Monographs</em>. <br> Oxford University Press, 1995. <dt><a name="Joh97"><b>[Joh97]</b></a><dd> D. L. Johnson. <br> <em>Presentations of groups</em>. <br> Cambridge University Press, Cambridge, second edition, 1997. <dt><a name="Kaup92"><b>[Kaup92]</b></a><dd> Ansgar Kaup. <br> Gitterbasen und Charaktere endlicher Gruppen. <br> Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1992. <dt><a name="KleidmanLiebeck90"><b>[KleidmanLiebeck90]</b></a><dd> Peter Kleidman and Martin Liebeck. <br> <em>The subgroup structure of the finite classical groups</em>. <br> Cambridge University Press, 1990. <dt><a name="Klimyk66"><b>[Klimyk66]</b></a><dd> A. U. Klimyk. <br> Decomposition of the direct product of irreducible representations of semisimple Lie algebras into irreducible representations. <br> <em>Ukrain. Mat. \vZ.</em>, 18(5):19--27, 1966. <dt><a name="Klimyk68"><b>[Klimyk68]</b></a><dd> A. U. Klimyk. <br> Decomposition of a direct product of irreducible representations of a semisimple Lie algebra into irreducible representations. <br> In <em>American Mathematical Society Translations. Series 2</em>, volume 76, pages 63--73. American Mathematical Society, Providence, R.I., 1968. <dt><a name="KLM01"><b>[KLM01]</b></a><dd> Gregor Kemper, Frank L"ubeck, and Kay Magaard. <br> Matrix generators for the Ree groups \sp 2<i>G</i>\sb 2(<i>q</i>). <br> <em>Comm. Algebra</em>, 29(1):407--413, 2001. <dt><a name="TACP2"><b>[TACP2]</b></a><dd> Donald E. Knuth. <br> <em>The Art of Computer Programming, Volume 2: Seminumerical Algorithms</em>. <br> Addison-Wesley, third edition, 1998. <dt><a name="L03"><b>[L03]</b></a><dd> Frank Lübeck. <br> Conway polynomials for finite fields. <br> <a href="http://www.math.rwth-aachen.de:8001/~Frank.Luebeck/data/ConwayPol">http://www.math.rwth-aachen.de:8001/~Frank.Luebeck/data/ConwayPol</a>. <dt><a name="Leon91"><b>[Leon91]</b></a><dd> Jeffrey S. Leon. <br> Permutation group algorithms based on partitions, I: theory and algorithms. <br> <em>J. Symbolic Comput.</em>, 12:533--583, 1991. <dt><a name="LLL82"><b>[LLL82]</b></a><dd> A. K. Lenstra, H. W. Lenstra, and L. Lovász. <br> Factoring polynomials with rational coefficients. <br> <em>Math. Ann.</em>, 261:513--534, 1982. <dt><a name="SOGOS"><b>[SOGOS]</b></a><dd> R[einhard] Laue, J[oachim] Neubüser, and U[lrich] Schoenwaelder. <br> Algorithms for finite soluble groups and the SOGOS system. <br> In Atkinson <a href="#Durham1982"><cite>Durham1982</cite></a>, pages 105--135. <dt><a name="LP91"><b>[LP91]</b></a><dd> Klaus Lux and Herbert Pahlings. <br> Computational aspects of representation theory of finite groups. <br> In G. O. Michler and C. R. Ringel, editors, <em>Representation theory of finite groups and finite-dimensional algebras</em>, volume 95 of <em> Progress in Mathematics</em>, pages 37--64. Birkhäuser, Basel, 1991. <dt><a name="Mac81"><b>[Mac81]</b></a><dd> I. G. Macdonald. <br> Numbers of conjugacy classes in some finite classical groups. <br> <em>Bull. Austral. Math. Soc.</em>, 23(1):23--48, 1981. <dt><a name="MeckyNeubueser89"><b>[MeckyNeubueser89]</b></a><dd> M[atthias] Mecky and J[oachim] Neubüser. <br> Some remarks on the computation of conjugacy classes of soluble groups. <br> <em>Bull. Austral. Math. Soc.</em>, 40(2):281--292, 1989. <dt><a name="NOV04"><b>[NOV04]</b></a><dd> E.A. O'Brien M.F. Newman and M.R. Vaughan-Lee. <br> Groups and nilpotent lie rings whose order is the sixth of a prime. <br> <em>J. Alg.</em>, 278:383 -- 401, 2003. <dt><a name="MS85"><b>[MS85]</b></a><dd> John McKay and Leonard H. Soicher. <br> Computing Galois groups over the rationals. <br> <em>J. Number Theory</em>, 20:273--281, 1985. <dt><a name="Mur58"><b>[Mur58]</b></a><dd> F[rancis] D. Murnaghan. <br> The orthogonal and symplectic groups. <br> Communications Series A 13, Dublin Inst. Adv. Studies, 1958. <dt><a name="MV97"><b>[MV97]</b></a><dd> Meena Mahajan and V. Vinay. <br> Determinant: combinatorics, algorithms, and complexity. <br> <em>Chicago J. Theoret. Comput. Sci.</em>, pages Article 5, 26 pp. (electronic), 1997. <dt><a name="Neb95"><b>[Neb95]</b></a><dd> Gabriele Nebe. <br> <em>Endliche rationale Matrixgruppen vom Grad 24</em>. <br> Dissertation, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1995. <dt><a name="Neb96"><b>[Neb96]</b></a><dd> Gabriele Nebe. <br> Finite subgroups of <i>GL</i><sub><i>n</i></sub>(<b>Q</b>) for 25 ≤ <i>n</i> ≤ 31. <br> <em>Comm. Alg.</em>, 24 (7):2341--2397, 1996. <dt><a name="Neu82"><b>[Neu82]</b></a><dd> Joachim Neubüser. <br> An elementary introduction to coset table methods in computational group theory. <br> In Campbell and Robertson <a href="#GrpsStAndrews81"><cite>GrpsStAndrews81</cite></a>, pages 1--45. <dt><a name="neukirch"><b>[neukirch]</b></a><dd> Jürgen Neukirch. <br> <em>Algebraische Zahlentheorie</em>. <br> Springer, Berlin, Heidelberg and New York, 1992. <dt><a name="New77"><b>[New77]</b></a><dd> M[ichael] F. Newman. <br> Determination of groups of prime-power order. <br> In R. A. Bryce, J. Cossey, and M[ichael] F. Newman, editors, <em> Group theory, Proc. Miniconf., Austral. Nat. Univ., Canberra, 1975</em>, volume 573 of <em>Lecture Notes in Math.</em>, pages 73--84. Springer, Berlin, Heidelberg and New York, 1977. <dt><a name="New90"><b>[New90]</b></a><dd> M[ichael] F. Newman. <br> Proving a group infinite. <br> <em>Arch. Math. (Basel)</em>, 54(3):209--211, 1990. <dt><a name="NPbook95"><b>[NPbook95]</b></a><dd> G[abriele] Nebe and W[ilhelm] Plesken. <br> <em>Finite rational matrix groups</em>, volume 556 of <em>AMS Memoirs</em>. <br> American Mathematical Society, 1995. <dt><a name="NP95"><b>[NP95]</b></a><dd> G[abriele] Nebe and W[ilhelm] Plesken. <br> <em>Finite rational matrix groups of degree 16</em>, pages 74--144. <br> Volume 556 of <em>AMS Memoirs/</em> <a href="#NPbook95"><cite>NPbook95</cite></a>, 1995. <dt><a name="NPP84"><b>[NPP84]</b></a><dd> J[oachim] Neubüser, H[erbert] Pahlings, and W[ilhelm] Plesken. <br> CAS; design and use of a system for the handling of characters of finite groups. <br> In Atkinson <a href="#Durham1982"><cite>Durham1982</cite></a>, pages 195--247. <dt><a name="OBr90"><b>[OBr90]</b></a><dd> E[amonn] A. O'Brien. <br> The <i>p</i>-group generation algorithm. <br> <em>J. Symbolic Comput.</em>, 9:677--698, 1990. <dt><a name="OBr91"><b>[OBr91]</b></a><dd> E[amonn] A. O'Brien. <br> The groups of order 256. <br> <em>J. Algebra</em>, 143:219--235, 1991. <dt><a name="Pah93"><b>[Pah93]</b></a><dd> Herbert Pahlings. <br> On the Möbius function of a finite group. <br> <em>Arch. Math. (Basel)</em>, 60:7--14, 1993. <dt><a name="Par84"><b>[Par84]</b></a><dd> Richard Parker. <br> The Computer Calculation of Modular Characters (the <font face="Gill Sans,Helvetica,Arial">MeatAxe</font>). <br> In Atkinson <a href="#Durham1982"><cite>Durham1982</cite></a>, pages 267--274. <dt><a name="Pfe91"><b>[Pfe91]</b></a><dd> G. Pfeiffer. <br> Von Permutationscharakteren und Markentafeln. <br> Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, 1991. <dt><a name="Pfe97"><b>[Pfe97]</b></a><dd> G. Pfeiffer. <br> The Subgroups of <i>M</i><sub>24</sub>, or How to Compute the Table of Marks of a Finite Group. <br> <em>Experiment. Math.</em>, 6(3):247--270, 1997. <dt><a name="Ple85"><b>[Ple85]</b></a><dd> W[ilhelm] Plesken. <br> Finite unimodular groups of prime degree and circulants. <br> <em>J. Algebra</em>, 97:286--312, 1985. <dt><a name="Ple90"><b>[Ple90]</b></a><dd> W[ilhelm] Plesken. <br> Additive decompositions of positive integral quadratic forms. <br> The paper is available at Lehrstuhl B für Mathematik, Rheinisch Westfälische Technische Hochschule Aachen, may be it will be published in the near future, 1990. <dt><a name="PN95"><b>[PN95]</b></a><dd> W[ilhelm] Plesken and G[abriele] Nebe. <br> <em>Finite rational matrix groups</em>, pages 1--73. <br> Volume 556 of <em>AMS Memoirs/</em> <a href="#NPbook95"><cite>NPbook95</cite></a>, 1995. <dt><a name="Poh87"><b>[Poh87]</b></a><dd> M[ichael] Pohst. <br> A modification of the LLL reduction algorithm. <br> <em>J. Symbolic Comput.</em>, 4:123--127, 1987. <dt><a name="PP77"><b>[PP77]</b></a><dd> Wilhelm Plesken and Michael Pohst. <br> On maximal finite irreducible subgroups of GL(n,Z). I. the five and seven dimensional cases, II. the six dimensional case. <br> <em>Math. Comp.</em>, 31:536--576, 1977. <dt><a name="PP80"><b>[PP80]</b></a><dd> Wilhelm Plesken and Michael Pohst. <br> On maximal finite irreducible subgroups of GL(n,Z). III. the nine dimensional case, IV. remarks on even dimensions with application to n = 8, V. the eight dimensional case and a complete description of dimensions less than ten. <br> <em>Math. Comp.</em>, 34:245--301, 1980. <dt><a name="RoneyDougal05"><b>[RoneyDougal05]</b></a><dd> Colva M. Roney-Dougal. <br> The primitive permutation groups of degree less than 2500. <br> <em>To appear in Journal of Algebra</em>, 2005. <dt><a name="RoneyDougal02"><b>[RoneyDougal02]</b></a><dd> Colva M. Roney-Dougal and William R. Unger. <br> The affine primitive permutation groups of degree less than 1000. <br> <em>Journal of Symbolic Computation</em>, 35:421--439, 2003. <dt><a name="Rin93"><b>[Rin93]</b></a><dd> Michael Ringe. <br> <em>The C MeatAxe, Release 1.5</em>. <br> Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1993. <dt><a name="Rob88"><b>[Rob88]</b></a><dd> E[dmund] F. Robertson. <br> Tietze transformations with weighted substring search. <br> <em>J. Symbolic Comput.</em>, 6:59--64, 1988. <dt><a name="Roy87"><b>[Roy87]</b></a><dd> Gordon F. Royle. <br> The transitive groups of degree twelve. <br> <em>J. Symbolic Comput.</em>, pages 255--268, 1987. <dt><a name="Sch90"><b>[Sch90]</b></a><dd> Gerhard J. A. Schneider. <br> Dixon's character table algorithm revisited. <br> <em>J. Symbolic Comput.</em>, 9:601--606, 1990. <dt><a name="Scherner92"><b>[Scherner92]</b></a><dd> Michael Scherner. <br> Erweiterung einer Arithmetik von Kreisteilungsk&accentuml;127 orpern auf deren Teilkörper und deren Implementation in GAP. <br> Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1992. <dt><a name="Schiffer94"><b>[Schiffer94]</b></a><dd> Ute Schiffer. <br> Cliffordmatrizen. <br> Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1994. <dt><a name="Sco73"><b>[Sco73]</b></a><dd> L. L. Scott. <br> Modular permutation representations. <br> <em>Trans. Amer. Math. Soc.</em>, 175:101--121, 1973. <dt><a name="Sho92"><b>[Sho92]</b></a><dd> Mark W. Short. <br> <em>The Primitive Soluble Permutation Groups of Degree less than 256</em>, volume 1519 of <em>Lecture Notes in Math.</em> <br> Springer, Berlin, Heidelberg and New York, 1992. <dt><a name="Sim70"><b>[Sim70]</b></a><dd> Charles C. Sims. <br> Computational methods in the study of permutation groups. <br> In John Leech, editor, <em>Computational Problems in Abstract Algebra, Proc. Conf. Oxford, 1967</em>, pages 169--183. Pergamon Press, Oxford, 1970. <dt><a name="Sims90b"><b>[Sims90b]</b></a><dd> Charles C. Sims. <br> Computing the order of a solvable permutation group. <br> <em>J. Symbolic Comput.</em>, 9:699--705, 1990. <dt><a name="Sims94"><b>[Sims94]</b></a><dd> C. C. Sims. <br> <em>Computation with Finitely Presented Groups</em>. <br> Cambridge University Press, 1994. <dt><a name="Sims97"><b>[Sims97]</b></a><dd> Charles C. Sims. <br> Computing with subgroups of automorphism groups of finite groups. <br> In Wolfgang Küchlin, editor, <em>Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation</em>, pages 40--403. The Association for Computing Machinery, ACM Press, 1997. <dt><a name="Sou94"><b>[Sou94]</b></a><dd> Bernd Souvignier. <br> Irreducible finite integral matrix groups of degree 8 and 10. <br> <em>Math. Comp.</em>, 63:335--350, 1994. <dt><a name="Spa89"><b>[Spa89]</b></a><dd> Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany. <br> <em>SPAS - Subgroup Presentation Algorithms System, version 2.5, User's reference manual</em>, 1989. <dt><a name="Tay87"><b>[Tay87]</b></a><dd> D. E. Taylor. <br> Pairs of generators for matrix groups. I. <br> <em>The Cayley Bulletin</em>, 3, 1987. <dt><a name="Theissen93"><b>[Theissen93]</b></a><dd> Heiko Theißen. <br> Methoden zur Bestimmung der rationalen Konjugiertheit in endlichen Gruppen. <br> Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, 1993. <dt><a name="Theissen97"><b>[Theissen97]</b></a><dd> Heiko Theißen. <br> <em>Eine Methode zur Normalisatorberechnung in Permutationsgruppen mit Anwendungen in der Konstruktion primitiver Gruppen</em>. <br> Dissertation, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1997. <dt><a name="vdW76"><b>[vdW76]</b></a><dd> Robert W. van der Waall. <br> On symplectic primitive modules and monomial groups. <br> <em>Indagationes Math.</em>, 38:362--375, 1976. <dt><a name="Wagon90"><b>[Wagon90]</b></a><dd> Stan Wagon. <br> Editor's corner: the Euclidean algorithm strikes again. <br> <em>Amer. Math. Monthly</em>, 97(2):125--129, 1990. <dt><a name="AGR"><b>[AGR]</b></a><dd> Robert A. Wilson. <br> ATLAS of Finite Group Representations. <br> <a href="http://www.mat.bham.ac.uk/atlas/">http://www.mat.bham.ac.uk/atlas/</a>. <dt><a name="Wil96"><b>[Wil96]</b></a><dd> R[obert] A. Wilson. <br> Standard generators for sporadic simple groups. <br> <em>J. Algebra</em>, 184:505--515, 1996. <dt><a name="Zagier90"><b>[Zagier90]</b></a><dd> D. Zagier. <br> A one-sentence proof that every prime <i>p</i> ≡ 1 mod 4 is a sum of two squares. <br> <em>Amer. Math. Monthly</em>, 97(2):144, 1990. <dt><a name="Zum89"><b>[Zum89]</b></a><dd> Matthias Zumbroich. <br> Grundlagen einer Arithmetik in Kreisteilungskörpern und ihre Implementation in CAS. <br> Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1989. </dl><p> [<a href="../index.htm">Top</a>] [<a href="chapters.htm">Up</a>]<p> <P> <font face="Gill Sans,Helvetica,Arial">GAP 4 manual<br>December 2008 </font></body></html>
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